Yes LAX-JFK-DFW-LAX would have to be it - can't do direct service LAX-JFk both ways.

ANother suggestion may be to have the starting point of the routing in SAN - you can either fly down to SAN (on a separate ticket) or drive down in a couple of hours (well at least the way I drive ) and start from there, thus:

SAN-->LAX
LAX --> JFK
JFK-->DFW-->LAX
LAX-->LHR
LHR --> BOM
Bom --> BKK
BKK --> SYD
SYD --> MEL
MEL --> SYD
SYD --> LAX

This would avoid any problem of going back to your point of origin (SAN start is similar to a SYD start if living in MEL.) And the SAN-LAX segment can be done at any time (maybe on a weekend) and not necessarily on the same day as LAX-JFK.